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Tom's address (Posted on 2002-05-30)

John is tryng to locate Tom's house. All he knows is that Tom lives on a street with houses numbered from 8 to 100.

John asks Tom:

"Is your house number bigger than 50?"

Tom answers him, but he lies. (John doesn't know that he's lying) John continues to ask:

"Is your house number a multiple of 4?"

Tom answers and again, he lies. Then John asks:

"Is your house number the square of an integer?"

Tom answres, but this time he tells the truth. Finally, John asks:

"Is the first digit of your house number 3?"

After Tom answers (we don't know if he lied or not) John declares Tom's house number, but he is wrong! What is Tom's house number?

Submitted by Half-Mad

Rating: 4.2857 (14 votes)

Solution: (Hide)

Tom's house number is 81. Since John asked if the first digit is 3, he thought the number was smaller than 50, but we know that Tom lied about that, so the number we're looking for is bigger than 50. After John asked that, he was certain he had the number, so that means that Tom must have said that the number was indeed the square of an integer, and is a multiple of 4. (That is the only way John could have narrowd down his options to only one) Since he lied about being a multiple of 4, and told the truth about being the square of an integer, we now know that his house number is bigger than 50, isn't a multiple of 4, and is the square of an integer. The only number between 8-100 that fits that description is 81.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
answer	K Sengupta	2008-02-14 14:48:23
Solution	Dej Mar	2008-02-14 03:43:36
Solution method suggestion	Rebecca Jaffe	2005-09-16 07:18:06
re: Eureka oops	Cassandra Wallace	2003-02-12 17:20:08
Eureka	Cassandra Wallace	2003-02-12 17:16:55
re: The answer is...	Freshter	2002-05-31 22:16:47
The answer is...	Freshter	2002-05-31 22:12:11
My guess	Happy	2002-05-30 12:02:28
Two storey complex (hints only -- solution to follow)	TomM	2002-05-30 12:00:38

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